327 research outputs found
Certifying Bimanual RRT Motion Plans in a Second
We present an efficient method for certifying non-collision for
piecewise-polynomial motion plans in algebraic reparametrizations of
configuration space. Such motion plans include those generated by popular
randomized methods including RRTs and PRMs, as well as those generated by many
methods in trajectory optimization. Based on Sums-of-Squares optimization, our
method provides exact, rigorous certificates of non-collision; it can never
falsely claim that a motion plan containing collisions is collision-free. We
demonstrate that our formulation is practical for real world deployment,
certifying the safety of a twelve degree of freedom motion plan in just over a
second. Moreover, the method is capable of discriminating the safety or lack
thereof of two motion plans which differ by only millimeters.Comment: 7 pages, 5 figures, 1 tabl
Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations
We resolve the local semistable reduction problem for overconvergent
F-isocrystals at monomial valuations (Abhyankar valuations of height 1 and
residue transcendence degree 0). We first introduce a higher-dimensional
analogue of the generic radius of convergence for a p-adic differential module,
which obeys a convexity property. We then combine this convexity property with
a form of the p-adic local monodromy theorem for so-called fake annuli.Comment: 36 pages; v3: refereed version; adds appendix with two example
Coleman maps and the p-adic regulator
This paper is a sequel to our earlier paper "Wach modules and Iwasawa theory
for modular forms" (arXiv: 0912.1263), where we defined a family of Coleman
maps for a crystalline representation of the Galois group of Qp with
nonnegative Hodge-Tate weights. In this paper, we study these Coleman maps
using Perrin-Riou's p-adic regulator L_V. Denote by H(\Gamma) the algebra of
Qp-valued distributions on \Gamma = Gal(Qp(\mu (p^\infty) / Qp). Our first
result determines the H(\Gamma)-elementary divisors of the quotient of
D_{cris}(V) \otimes H(\Gamma) by the H(\Gamma)-submodule generated by (\phi *
N(V))^{\psi = 0}, where N(V) is the Wach module of V. By comparing the
determinant of this map with that of L_V (which can be computed via
Perrin-Riou's explicit reciprocity law), we obtain a precise description of the
images of the Coleman maps. In the case when V arises from a modular form, we
get some stronger results about the integral Coleman maps, and we can remove
many technical assumptions that were required in our previous work in order to
reformulate Kato's main conjecture in terms of cotorsion Selmer groups and
bounded p-adic L-functions.Comment: 27 page
Adelic versions of the Weierstrass approximation theorem
Let be a compact subset of
and denote by
the ring of continuous
functions from into . We obtain two kinds
of adelic versions of the Weierstrass approximation theorem. Firstly, we prove
that the ring is dense in the
direct product for the
uniform convergence topology. Secondly, under the hypothesis that, for each
, for all but finitely many , we prove the
existence of regular bases of the -module , and show that, for such
a basis , every function in
may be uniquely written
as a series where
and .Comment: minor corrections the statement of Theorem 3.5, which covers the case
of a general compact subset of the profinite completion of Z. to appear in
Journal of Pure and Applied Algebra, comments are welcome
Etude sur le réchauffement de la viande au cours de la fabrication de Bœuf assaisonné pendant la saison chaude
Dumeste Marcel H., Amice J. Étude sur le réchauffement de la viande au cours de la fabrication du Bœuf assaisonné pendant la saison chaude (2 graphiques). In: Bulletin de l'Académie Vétérinaire de France tome 110 n°5, 1957. pp. 195-202
<i>p</i>-adic asymptotic properties of constant-recursive sequences
In this article we study p-adic properties of sequences of integers (or p-adic integers) that satisfy a linear recurrence with constant coefficients. For such a sequence, we give an explicit approximate twisted interpolation to ℤp. We then use this interpolation for two applications. The first is that certain subsequences of constant-recursive sequences converge p-adically. The second is that the density of the residues modulo pα attained by a constant-recursive sequence converges, as α→∞, to the Haar measure of a certain subset of ℤp. To illustrate these results, we determine some particular limits for the Fibonacci sequence
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